What is the integral from 0 to 1-y of 24xy ?

The integral from 0 to 1-y of 24xy is 12y(-y+1)^2

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integral from 0 to 1-y of 24xy

\int_{0}^{1 - y} 24 x y d x

12 y (- y + 1)^{2}

Solution steps

\int_{0}^{1 - y} 24 x y d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 24 y \cdot \int_{0}^{1 - y} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{1 - y}

= 24 y [\frac{x ^{2}}{2}]_{0}^{1 - y}

Compute the boundaries:

\frac{( - y + 1 ) ^{2}}{2}

= 24 y \frac{( - y + 1 ) ^{2}}{2}

Simplify

= 12 y (- y + 1)^{2}

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What is the integral from 0 to 1-y of 24xy ?
The integral from 0 to 1-y of 24xy is 12y(-y+1)^2